DOI 10.1140/epjc/s10052-012-1869-5
Regular Article - Experimental Physics
Exclusive electroproduction of two pions at HERA
The ZEUS CollaborationH. Abramowicz45,ah, I. Abt35, L. Adamczyk13, M. Adamus54, R. Aggarwal7,d, S. Antonelli4, P. Antonioli3, A. Antonov33, M. Arneodo50, D. Ashery45, V. Aushev26,27,z, Y. Aushev27,z,aa, O. Bachynska15, A. Bamberger19,
A.N. Barakbaev25, G. Barbagli17, G. Bari3, F. Barreiro30, N. Bartosik27,ab, D. Bartsch5, M. Basile4, O. Behnke15, J. Behr15, U. Behrens15, L. Bellagamba3, A. Bertolin39, S. Bhadra57, M. Bindi4, C. Blohm15, V. Bokhonov26,z, T. Bołd13, K. Bondarenko27, E.G. Boos25, K. Borras15, D. Boscherini3, D. Bot15, I. Brock5, E. Brownson56,
R. Brugnera40, N. Brümmer37, A. Bruni3, G. Bruni3, B. Brzozowska53, P.J. Bussey20, B. Bylsma37, A. Caldwell35, M. Capua8, R. Carlin40, C.D. Catterall57, S. Chekanov1, J. Chwastowski12,f, J. Ciborowski53,al, R. Ciesielski15,h, L. Cifarelli4, F. Cindolo3, A. Contin4, A.M. Cooper-Sarkar38, N. Coppola15,i, M. Corradi3, F. Corriveau31, M. Costa49, G. D’Agostini43, F. Dal Corso39, J. del Peso30, R.K. Dementiev34, S. De Pasquale4,b, M. Derrick1, R.C.E. Devenish38, D. Dobur19,t, B.A. Dolgoshein33,†, G. Dolinska26,27, A.T. Doyle20, V. Drugakov16, L.S. Durkin37, S. Dusini39, Y. Eisenberg55, P.F. Ermolov34,†, S. Eskreys12,†, S. Fang15,j, S. Fazio8, J. Ferrando38, M.I. Ferrero49, J. Figiel12, M. Forrest20,w, B. Foster38,ad, G. Gach13, A. Galas12, E. Gallo17, A. Garfagnini40, A. Geiser15,
I. Gialas21,x, L.K. Gladilin34,ac, D. Gladkov33, C. Glasman30, O. Gogota26,27, Yu.A. Golubkov34, P. Göttlicher15,k, I. Grabowska-Bołd13, J. Grebenyuk15, I. Gregor15, G. Grigorescu36, G. Grzelak53, O. Gueta45, E. Gurvich45, M. Guzik13, C. Gwenlan38,ae, T. Haas15, W. Hain15, R. Hamatsu48, J.C. Hart44, H. Hartmann5, G. Hartner57, E. Hilger5, D. Hochman55, R. Hori47, K. Horton38,af, A. Hüttmann15, Z.A. Ibrahim10, Y. Iga42, R. Ingbir45, M. Ishitsuka46, H.-P. Jakob5, F. Januschek15, T.W. Jones52, M. Jüngst5, I. Kadenko27, B. Kahle15, S. Kananov45, T. Kanno46, U. Karshon55, F. Karstens19,u, I.I. Katkov15,l, M. Kaur7, P. Kaur7,d, A. Keramidas36, L.A. Khein34, J.Y. Kim9, D. Kisielewska13, S. Kitamura48,aj, R. Klanner22, U. Klein15,m, E. Koffeman36, P. Kooijman36,
Ie. Korol26,27, I.A. Korzhavina34,ac, A. Kota ´nski14,g, U. Kötz15, H. Kowalski15, O. Kuprash15, M. Kuze46, A. Lee37, B.B. Levchenko34, A. Levy45,a, V. Libov15, S. Limentani40, T.Y. Ling37, M. Lisovyi15, E. Lobodzinska15,
W. Lohmann16, B. Löhr15, E. Lohrmann22, K.R. Long23, A. Longhin39, D. Lontkovskyi15, O.Yu. Lukina34, J. Maeda46,ai, S. Magill1, I. Makarenko15, J. Malka15, R. Mankel15, A. Margotti3, G. Marini43, J.F. Martin51, A. Mastroberardino8, M.C.K. Mattingly2, I.-A. Melzer-Pellmann15, S. Mergelmeyer5, S. Miglioranzi15,n, F. Mohamad Idris10, V. Monaco49, A. Montanari15, J.D. Morris6,c, K. Mujkic15,o, B. Musgrave1, K. Nagano24, T. Namsoo15,p, R. Nania3, A. Nigro43, Y. Ning11, T. Nobe46, U. Noor57, D. Notz15, R.J. Nowak53, A.E. Nuncio-Quiroz5, B.Y. Oh41, N. Okazaki47, K. Oliver38, K. Olkiewicz12, Yu. Onishchuk27, K. Papageorgiu21, A. Parenti15, E. Paul5,
J.M. Pawlak53, B. Pawlik12, P.G. Pelfer18, A. Pellegrino36, W. Perla ´nski53,am, H. Perrey15, K. Piotrzkowski29, P. Pluci ´nski54,an, N.S. Pokrovskiy25, A. Polini3, A.S. Proskuryakov34, M. Przybycie ´n13, A. Raval15, D.D. Reeder56, B. Reisert35, Z. Ren11, J. Repond1, Y.D. Ri48,ak, A. Robertson38, P. Roloff15,n, I. Rubinsky15, M. Ruspa50, R. Sacchi49,
A. Salii27, U. Samson5, G. Sartorelli4, A.A. Savin56, D.H. Saxon20, M. Schioppa8, S. Schlenstedt16, P. Schleper22, W.B. Schmidke35, U. Schneekloth15, V. Schönberg5, T. Schörner-Sadenius15, J. Schwartz31, F. Sciulli11,
L.M. Shcheglova34, R. Shehzadi5, S. Shimizu47,n, I. Singh7,d, I.O. Skillicorn20, W. Słomi ´nski14, W.H. Smith56, V. Sola49, A. Solano49, D. Son28, V. Sosnovtsev33, A. Spiridonov15,q, H. Stadie22, L. Stanco39, A. Stern45,
T.P. Stewart51, A. Stifutkin33, P. Stopa12, S. Suchkov33, G. Susinno8, L. Suszycki13, J. Sztuk-Dambietz22, D. Szuba22, J. Szuba15,r, A.D. Tapper23, E. Tassi8,e, J. Terrón30, T. Theedt15, H. Tiecke36, K. Tokushuku24,y, O. Tomalak27, J. Tomaszewska15,s, T. Tsurugai32, M. Turcato22, T. Tymieniecka54,ao, M. Vázquez36,n, A. Verbytskyi15, O. Viazlo26,27, N.N. Vlasov19,v, O. Volynets27, R. Walczak38, W.A.T. Wan Abdullah10, J.J. Whitmore41,ag,
L. Wiggers36, M. Wing52, M. Wlasenko5, G. Wolf15, H. Wolfe56, K. Wrona15, A.G. Yagües-Molina15, S. Yamada24, Y. Yamazaki24,z, R. Yoshida1, C. Youngman15, A.F. ˙Zarnecki53, L. Zawiejski12, O. Zenaiev15, W. Zeuner15,n, B.O. Zhautykov25, N. Zhmak26,z, C. Zhou31, A. Zichichi4, Z. Zolkapli10, M. Zolko27, D.S. Zotkin34
1Argonne National Laboratory, Argonne, IL 60439-4815, USAA
2Andrews University, Berrien Springs, MI 49104-0380, USA 3INFN Bologna, Bologna, ItalyB
4University and INFN Bologna, Bologna, ItalyB
5Physikalisches Institut der Universität Bonn, Bonn, GermanyC
6H.H. Wills Physics Laboratory, University of Bristol, Bristol, UKD
7
Panjab University, Department of Physics, Chandigarh, India 8
Calabria University, Physics Department and INFN, Cosenza, ItalyB
9
Institute for Universe and Elementary Particles, Chonnam National University, Kwangju, South Korea 10
Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, MalaysiaE
11
Nevis Laboratories, Columbia University, Irvington on Hudson, NY 10027, USAF
12
The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, PolandG
13
AGH-University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, PolandH 14
Department of Physics, Jagellonian University, Cracow, Poland 15
Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany 16
Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany 17
INFN Florence, Florence, ItalyB 18
University and INFN Florence, Florence, ItalyB 19
Fakultät für Physik der Universität Freiburg i.Br., Freiburg i.Br., Germany 20
School of Physics and Astronomy, University of Glasgow, Glasgow, UKD 21
Department of Engineering in Management and Finance, Univ. of the Aegean, Chios, Greece 22Hamburg University, Institute of Experimental Physics, Hamburg, GermanyI
23Imperial College London, High Energy Nuclear Physics Group, London, UKD
24Institute of Particle and Nuclear Studies, KEK, Tsukuba, JapanJ
25
Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan 26
Institute for Nuclear Research, National Academy of Sciences, Kyiv, Ukraine 27
Department of Nuclear Physics, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine 28
Kyungpook National University, Center for High Energy Physics, Daegu, South KoreaK
29
Institut de Physique Nucléaire, Université Catholique de Louvain, Louvain-la-Neuve, BelgiumL
30
Departamento de Física Teórica, Universidad Autónoma de Madrid, Madrid, SpainM
31
Department of Physics, McGill University, Montréal, Québec, Canada H3A 2T8N 32
Meiji Gakuin University, Faculty of General Education, Yokohama, JapanJ 33
Moscow Engineering Physics Institute, Moscow, RussiaO 34
Moscow State University, Institute of Nuclear Physics, Moscow, RussiaP 35
Max-Planck-Institut für Physik, München, Germany 36
NIKHEF and University of Amsterdam, Amsterdam, NetherlandsQ 37
Physics Department, Ohio State University, Columbus, OH 43210, USAA 38
Department of Physics, University of Oxford, Oxford, UKD 39
INFN Padova, Padova, ItalyB
40Dipartimento di Fisica dell’ Università and INFN, Padova, ItalyB
41Department of Physics, Pennsylvania State University, University Park, PA 16802, USAF
42Polytechnic University, Sagamihara, JapanJ
43
Dipartimento di Fisica, Università ‘La Sapienza’ and INFN, Rome, ItalyB
44
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UKD
45
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv, IsraelR
46
Department of Physics, Tokyo Institute of Technology, Tokyo, JapanJ
47
Department of Physics, University of Tokyo, Tokyo, JapanJ
48
Tokyo Metropolitan University, Department of Physics, Tokyo, JapanJ
49
Università di Torino and INFN, Torino, ItalyB 50
Università del Piemonte Orientale, Novara, and INFN, Torino, ItalyB 51
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7N 52
Physics and Astronomy Department, University College London, London, UKD 53
Faculty of Physics, University of Warsaw, Warsaw, Poland 54
National Centre for Nuclear Research, Warsaw, Poland 55
Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot, Israel 56
Department of Physics, University of Wisconsin, Madison, WI 53706, USAA 57Department of Physics, York University, Toronto, Ontario, Canada M3J 1P3N
Received: 21 November 2011 / Published online: 25 January 2012
© The Author(s) 2012. This article is published with open access at Springerlink.com
Abstract The exclusive electroproduction of two pions in the mass range 0.4 < Mπ π<2.5 GeV has been studied with the ZEUS detector at HERA using an integrated luminos-ity of 82 pb−1. The analysis was carried out in the
kine-matic range of 2 < Q2<80 GeV2, 32 < W < 180 GeV and|t| < 0.6 GeV2, where Q2 is the photon virtuality, W is the photon-proton centre-of-mass energy and t is the squared four-momentum transfer at the proton vertex. The
two-pion invariant-mass distribution is interpreted in terms of the pion electromagnetic form factor,|F (Mπ π)|, assum-ing that the studied mass range includes the contributions of the ρ, ρ and ρ vector-meson states. The masses and widths of the resonances were obtained and the Q2 depen-dence of the cross-section ratios σ (ρ→ ππ)/σ (ρ) and σ (ρ→ ππ)/σ (ρ) was extracted. The pion form factor ob-tained in the present analysis is compared to that obob-tained in e+e−→ π+π−.
ae-mail:[email protected]
ASupported by the US Department of Energy
BSupported by the Italian National Institute for Nuclear Physics (INFN)
CSupported by the German Federal Ministry for Education and Re-search (BMBF), under contract No. 05 H09PDF
DSupported by the Science and Technology Facilities Council, UK ESupported by an FRGS grant from the Malaysian government FSupported by the US National Science Foundation. Any opinion, find-ings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation
GSupported by the Polish Ministry of Science and Higher Education as a scientific project No. DPN/N188/DESY/2009
HSupported by the Polish Ministry of Science and Higher Education and its grants for Scientific Research
ISupported by the German Federal Ministry for Education and Re-search (BMBF), under contract No. 05h09GUF, and the SFB 676 of the Deutsche Forschungsgemeinschaft (DFG)
JSupported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research KSupported by the Korean Ministry of Education and Korea Science and Engineering Foundation
LSupported by FNRS and its associated funds (IISN and FRIA) and by an Inter-University Attraction Poles Programme subsidised by the Belgian Federal Science Policy Office
MSupported by the Spanish Ministry of Education and Science through funds provided by CICYT
NSupported by the Natural Sciences and Engineering Research Coun-cil of Canada (NSERC)
OPartially supported by the German Federal Ministry for Education and Research (BMBF)
PSupported by RF Presidential grant N 4142.2010.2 for Leading Sci-entific Schools, by the Russian Ministry of Education and Science through its grant for Scientific Research on High Energy Physics and under contract No.02.740.11.0244
QSupported by the Netherlands Foundation for Research on Matter (FOM)
RSupported by the Israel Science Foundation bNow at University of Salerno, Italy
cNow at Queen Mary University of London, United Kingdom dAlso funded by Max Planck Institute for Physics, Munich, Germany eAlso Senior Alexander von Humboldt Research Fellow at Hamburg University, Institute of Experimental Physics, Hamburg, Germany
1 Introduction
Exclusive electroproduction of vector mesons takes place through a virtual photon γ∗ by means of the process γ∗p→ Vp. At large values of the centre-of-mass energy, W, this is usually viewed as a three-step process; the vir-tual photon γ∗ fluctuates into a q¯q pair which interacts with the proton through a two-gluon ladder and hadronizes into a vector meson, V . The production of ground-state vector mesons, V = ρ, ω, φ, J/ψ, Υ , which are 1S triplet fAlso at Cracow University of Technology, Faculty of Physics, Mathe-mathics and Applied Computer Science, Poland
gSupported by the research grant No. 1 P03B 04529 (2005–2008) hNow at Rockefeller University, New York, NY 10065, USA iNow at DESY group FS-CFEL-1
jNow at Institute of High Energy Physics, Beijing, China kNow at DESY group FEB, Hamburg, Germany lAlso at Moscow State University, Russia mNow at University of Liverpool, UK nNow at CERN, Geneva, Switzerland
oAlso affiliated with University College London, UK pNow at Goldman Sachs, London, UK
qAlso at Institute of Theoretical and Experimental Physics, Moscow, Russia
rAlso at FPACS, AGH-UST, Cracow, Poland sPartially supported by Warsaw University, Poland
tNow at Istituto Nucleare di Fisica Nazionale (INFN), Pisa, Italy uNow at Haase Energie Technik AG, Neumünster, Germany vNow at Department of Physics, University of Bonn, Germany wNow at Biodiversität und Klimaforschungszentrum (BiK-F), Frank-furt, Germany
xAlso affiliated with DESY, Germany yAlso at University of Tokyo, Japan zNow at Kobe University, Japan zSupported by DESY, Germany †Deceased
aaMember of National Technical University of Ukraine, Kyiv Polytech-nic Institute, Kyiv, Ukraine
abMember of National University of Kyiv–Mohyla Academy, Kyiv, Ukraine
acPartly supported by the Russian Foundation for Basic Research, grant 11-02-91345-DFG_a
adAlexander von Humboldt Professor; also at DESY and University of Oxford
aeSTFC Advanced Fellow afNee Korcsak-Gorzo
agThis material was based on work supported by the National Science Foundation, while working at the Foundation
ahAlso at Max Planck Institute for Physics, Munich, Germany, External Scientific Member
aiNow at Tokyo Metropolitan University, Japan ajNow at Nihon Institute of Medical Science, Japan akNow at Osaka University, Osaka, Japan
q¯q states, has been extensively studied at HERA, particu-larly in several recent publications [1–10]. As the virtual-ity, Q2, of the photon increases, the process becomes hard and can be calculated in perturbative Quantum Chromody-namics (pQCD). Furthermore, by varying Q2, and thus the size of the q¯q pair, sensitivity to the vector-meson wave-function can be obtained by scanning it at different q¯q dis-tance scales. Expectations in the QCD framework vary from calculations based only on the mass properties and typical size of the q¯q inside the vector-meson [11,12], to those based on the details of the vector meson wave-function de-pendence on the size of the q¯q pair [13–17]. The approaches differ in their predictions for the Q2dependence of the cross sections for excited vector-meson states and their ratio to their ground state.
The only radially excited 2S triplet q¯q state studied at HERA so far has been the ψ(2S) state [18]. In this study, only the photoproduction reaction was investigated and the low cross-section ratio of ψ(2S) to the ground-state J /ψ supported the existence of a suppression effect, expected if a node in the ψ(2S) wave-function is present.
Other excited vector-meson states, in particular those consisting of light quarks, can be used to study the effect caused by changing the scanning size. Exclusive π+π− pro-duction has been measured previously in the annihilation process e+e−→ π+π− [19], as well as in photoproduc-tion [20]. The π+π− mass distribution shows a complex structure in the mass range 1–2 GeV. Evidence for two ex-cited vector-meson states has been established [21,22]; the ρ(1450) is assumed to be predominantly a radially excited 2S state and the ρ(1700) is an orbitally excited 2D state, with some mixture of the S and D waves [23]. In addition there is also the ρ3(1690) spin-3 meson [24] which has a π π decay mode. The two-pion decay mode of these resonances is related [25,26] to the pion electromagnetic form factor, Fπ(Mπ π).
In this paper, a study of exclusive electroproduction of two pions,
γ∗p→ π+π−p, (1)
is presented in the two-pion mass range 0.4 < Mπ π < 2.5 GeV, in the kinematic range 2 < Q2<80 GeV2, 32 < W <180 GeV and|t| < 0.6 GeV2, where t is the squared four-momentum transfer at the proton vertex. The Mπ π sys-tem consists of a resonance part and a non-resonant back-ground. The resonances are described by the pion form fac-tor. The contributions of the three vector-mesons ρ, ρ and
alAlso at Łód´z University, Poland amMember of Łód´z University, Poland
anNow at Department of Physics, Stockholm University, Stockholm, Sweden
aoAlso at Cardinal Stefan Wyszy´nski University, Warsaw, Poland
ρare extracted and their relative rates as a function of Q2 are discussed in terms of QCD expectations.
2 The pion form factor
The two-pion invariant-mass distribution of (1), after sub-traction of the non-resonant background,1can be related to the pion electromagnetic form factor, Fπ(Mπ π), through the following relation [25,26]:
dN (Mπ π)
dMπ π ∝Fπ(Mπ π) 2
. (2)
There are several parameterizations of the pion form factor usually used for fitting the π+π− mass distribu-tion; the Kuhn-Santamaria (KS) [27], the Gounaris-Sakurai (GS) [28] and the Hidden Local Symmetry (HLS) [29,30] parameterizations. In this paper, results based on the KS pa-rameterization are presented.
In the mass range Mπ π<2.5 GeV, the KS parameteriza-tion of the pion form factor includes contribuparameteriza-tions from the ρ(770), ρ(1450) and ρ(1700) resonances,2
Fπ(Mπ π)=BWρ(Mπ π)+ βBWρ(Mπ π)+ γ BWρ(Mπ π)
1+ β + γ .
(3)
Here β and γ are relative amplitudes and BWV is the Breit-Wigner distribution which has the form
BWV(Mπ π)=
MV2 MV2− M2
π π− iMVΓV(Mπ π)
, (4)
where MV and ΓV(Mπ π)are the vector-meson mass and momentum-dependent width, respectively. The latter has the form ΓV(Mπ π)= ΓV pπ(Mπ π) pπ(MV) 3M2 V M2 π π , (5)
where ΓV is the width of the V meson at Mπ π = MV, pπ(Mπ π)= 1/2M2
π π− 4Mπ2 is the pion momentum in the π+π−centre-of-mass frame, pπ(MV)is the pion mo-mentum in the V -meson rest frame, and Mπ is the pion mass.
1This is assumed not to interfere with the resonance signal.
2This analysis cannot distinguish between ρ3(1690) and ρ(1700).
Theoretical calculations estimate the contribution of ρ3(1690) to be either one order of magnitude [12] or 2–5 times [31] smaller than that of the ρ(1700).
3 Experimental set-up
The analyzed data were collected with the ZEUS detector at the HERA collider in the years 1998–2000, when 920 GeV protons collided with 27.5 GeV electrons or positrons. The sample used for this study corresponds to 81.7 pb−1 of which 65.0 pb−1were collected with an e+and the rest with an e−beam.3
A detailed description of the ZEUS detector can be found elsewhere [32]. A brief outline of the components that are most relevant for this analysis is given below.
The charged particles were tracked in the central tracking detector (CTD) [33–35] which operated in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The CTD consisted of 72 cylindrical drift chamber layers, orga-nized in nine superlayers covering the polar-angle4region 15◦< θ <164◦. The transverse-momentum resolution for full-length tracks was σ (pT)/pT = 0.0058pT ⊕ 0.0065 ⊕ 0.0014/pT, with pT in GeV.
The scattered electron was identified in the high-resolu-tion uranium–scintillator calorimeter (CAL) [36–39] which covered 99.7% of the total solid angle and consisted of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part was subdivided trans-versely into towers and longitudinally into one electromag-netic section (EMC) and either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC). The CAL en-ergy resolution, as measured under test-beam conditions, was σ (E)/E = 0.18/√E for electrons and σ (E)/E = 0.35/√Efor hadrons, with E in GeV.
The position of the scattered electron was determined by combining information from the CAL, the small-angle rear tracking detector [40] and the hadron-electron separa-tor [41].
The luminosity was measured from the rate of the bremsstrahlung process ep→ eγ p. The photon was mea-sured in a lead–scintillator calorimeter [42–44] placed in the HERA tunnel at Z= −107 m.
4 Data selection and reconstruction
The online event selection required an electron candidate in the CAL, along with the detection of at least one and not more than six tracks in the CTD.
In the offline selection, the following further require-ments were imposed:
3From now on, electrons and positrons will be both referred to as elec-trons in this paper.
4The ZEUS coordinate system is a right-handed Cartesian system, with the Z axis pointing in the proton beam direction, referred to as the “forward direction”, and the X axis pointing left towards the centre of HERA. The coordinate origin is at the nominal interaction point. The polar angle, θ , is measured with respect to the proton beam direction.
• the presence of a scattered electron, with energy in the CAL greater that 10 GeV and with an impact point on the face of the RCAL outside a rectangular area of 26.4× 16 cm2in the X–Y plane;
• the Z coordinate of the interaction vertex was within ±50 cm of the nominal interaction point;
• in addition to the scattered electron, the presence of ex-actly two oppositely charged tracks. Both tracks have to be associated with the reconstructed vertex, each having pseudorapidity|η| less than 1.75 and transverse momen-tum greater that 150 MeV. This ensures high reconstruc-tion efficiency and excellent momentum resolureconstruc-tion in the CTD. These tracks were treated in the following analysis as a π+π−pair;
• E − PZ>45 GeV, where E− PZ=
i(Ei− PZi)and
the summation is over the energy Ei and longitudinal mo-mentum PZiof the final-state electron and pions. This cut
excludes events with high-energy photons radiated in the initial state;
• events with any energy deposit larger than 300 MeV in the CAL, not associated with the pion tracks (so-called ‘unmatched islands’), were rejected.
The following kinematic variables are used to describe the exclusive production of a π+π−pair:
• Q2, the four-momentum squared of the virtual photon; • W2, the squared centre-of-mass energy of the
photon-proton system;
• Mπ π, the invariant mass of the two pions;
• t, the squared four-momentum transfer at the proton ver-tex;
• Φh, the angle between the π+π− production plane and the positron scattering plane in the γ∗p centre-of-mass frame;
• θhand φh, the polar and azimuthal angles of the positively charged pion in the s-channel helicity frame [45] of the π+π−.
The kinematic variables were reconstructed using the so-called ‘constrained’ method [46], which uses the momenta of the decay particles measured in the CTD and the recon-structed polar and azimuthal angles of the scattered elec-tron. The analysis was restricted to the kinematic region 2 < Q2<80 GeV2, 32 < W < 180 GeV, |t| ≤ 0.6 GeV2 and 0.4 < Mπ π<2.5 GeV. The lower mass range excludes reflections from the φ→ K+K−decays and the upper limit excludes the J /ψ→ μ+μ−, e+e−decays with its radiative tail.
The above selection yielded 63517 events for this analy-sis.
The above cuts do not eliminate events in which the pro-ton dissociates into a low-mass final state, the products of which disappear down the beam pipe. This contribution, es-timated [2] to be about 20% in the range of this analysis,
was found to be Q2and W independent. Its presence does not affect the conclusions of this analysis.
5 Monte Carlo simulation
The program ZEUSVM[47] interfaced to HERACLES4.4 [48] was used. The effective distributions of Q2, W and|t| were parameterized to reproduce the data. The mass and angular distributions were generated uniformly and the MC events were then iteratively reweighted using the results of the anal-ysis.
The generated events were passed through a full simula-tion of the ZEUS detector based on GEANT 3.21 [49] and processed through the same chain of selection and recon-struction procedures as the data, accounting for trigger as well as detector acceptance and smearing effects. The num-ber of simulated events after reconstruction was approxi-mately seven times greater than the number of reconstructed data events.
A detailed comparison between the data and the ZEUSVM MC distributions for the mass range 0.65 < Mπ π<1.1 GeV has been presented elsewhere [2]. Some examples for the mass range 1.1 < Mπ π <2.1 GeV are shown here. The transverse momentum, pT, of the π+ and the π− parti-cles for different ranges of Q2 and Mπ π are presented in Fig. 1. Figure 2 shows the Q2, W , |t|, cos θh, φh, and Φhdistributions for events selected within the mass ranges 1.1 < Mπ π <1.6 GeV, while Fig.3 shows those distribu-tions for the mass range 1.6 < Mπ π<2.1 GeV. All mea-sured distributions are well described by the MC simula-tions.
6 The π π mass fit
The π+π− mass distribution, after acceptance correction determined from the above MC simulation, is shown in Fig.4. A clear peak is seen in the ρ mass range. A small shoulder is apparent around 1.3 GeV and a secondary peak at about 1.8 GeV.
The two-pion invariant-mass distribution was fitted, us-ing the least-square method [50], as a sum of two terms,
dN (Mπ π) dMπ π = A 1−4M 2 π M2 π π F π(Mπ π) 2 + B M0 Mπ π n , (6) where A is an overall normalization constant. The second term is a parameterization of the non-resonant background, with constant parameters B, n and M0= 1 GeV. The other parameters, the masses and widths of the three resonances and their relative contributions β and γ , enter through the
Fig. 1 Comparison between the data and the ZEUSVMMC
distribu-tions for the transverse momentum, pT, of π+and π−particles for different ranges of Q2 and Mπ π as indicated in the figure. The MC distributions are normalized to the data
pion form factor, Fπ (see (3)). The fit, which includes 11 parameters, gives a good description of the data (χ2/ndf= 28.8/24= 1.2). The result of the fit is shown in Fig.4 to-gether with the contribution of each of the two terms of (6). The ρ and the ρ signals are clearly visible. The negative interference between all the resonances results in the ρ sig-nal appearing as a shoulder. To illustrate this better, the same data and fit are shown in Fig.5on a linear scale and limited to Mπ π > 1.2 GeV, with separate contributions from the background, the three resonant amplitudes as well as their total interference term.
The fit parameters are listed in Table1. Also listed are the mass and width parameters from the Particle Data Group (PDG) [51]. The masses and widths of the ρ and the ρ as well as the width of the ρ agree with those listed in the PDG, while there is about 100 MeV difference between the PDG value and the fitted mass of the ρ. It should however be noted that the value quoted by PDG is an average over many measurements having a large spread (1265± 75 up to 1424± 25 MeV for the ππ decay mode) in this mass range. The measured negative value of β and positive value of γ implies that the relative signs of the amplitudes of the
Fig. 2 Comparison between the data and the ZEUSVMMC distribu-tions for Q2, W ,|t|, cos θh, Φh and φh for events within mass range 1.1 < Mπ π<1.6 GeV. The MC distributions are normalized to the data
Fig. 3 Comparison between the data and the ZEUSVMMC
distribu-tions for Q2, W ,|t|, cos θh, Φh and φh for events within mass range 1.6 < Mπ π<2.1 GeV. The MC distributions are normalized to the data
three resonances ρ, ρ and ρ are +, −, +, respectively. A similar pattern was observed in e+e−→ π+π− and τ -decay experiments [53–61], which also showed a dip in
Fig. 4 The two-pion invariant-mass distribution, Mπ π, where Nπ πis
the acceptance-corrected number of events in each bin of 60 MeV. The dots are the data and the full line is the result of a fit using the Kuhn-Santamaria parameterization. The dashed line is the result of the pion form factor normalized to the data and the dash-dotted line de-notes the background contribution
Fig. 5 The two-pion invariant-mass distribution, Mπ π, where Nπ πis
the acceptance corrected number of events in each bin of 60 MeV. The dots are the data and the full line is the result of a fit using the Kuhn-Santamaria parameterization. The contributions of the three res-onances ρ, ρ and ρ are shown as dashed, dash-dotted and dotted
lines, respectively. The sum of their interferences is shown by the long– dash-dotted line. The background is presented as the sparse dotted line
the mass range around 1.6 GeV, resulting from destruc-tive interference. There is a single experiment where a con-structive interference was obtained around 1.6 GeV, namely γp→ π+π−p[20], a result which is not understood [15].
In the mass fits above it was assumed that the relative am-plitudes β and γ are real. In order to test this assumption, the fit was repeated allowing them to be complex. The pion form factor was re-written in the form
Fπ(Mπ π)=
BWρ(Mπ π)+ β0· exp(iΦ12)BWρ(Mπ π)+ γ0· exp(iΦ13)BWρ(Mπ π) 1+ β0+ γ0
, (7)
where β0and γ0are real numbers and two additional fit pa-rameters, Φ12and Φ13, are the corresponding phase shifts. The value of the phase-shifts obtained from the fit were Φ12= 3.2 ± 0.2 rad and Φ13= 0.1 ± 0.2 rad, supporting the assumption of the real nature of the relative amplitudes.
7 Systematic uncertainties
The systematic uncertainties of the fit parameters were eval-uated by varying the selection cuts and the MC simulation parameters. Motivation for the variation in cuts used below can be found in a previous ZEUS analysis [2]. The following selection cuts were varied:
• the E − PZ cut was changed within the resolution of ±3 GeV;
• the pT threshold for the pion tracks (default 0.15 GeV) was increased to 0.2 GeV and the|η| cut on the two pion tracks was changed (default 1.75) by±0.25;
• the required maximum distance of closest approach of the two extrapolated pion tracks to the matched island in the CAL was changed from 30 cm to 20 cm;
• the Z-vertex cut was varied by ±10 cm;
Table 1 Fit parameters obtained using the Fπ(Mπ π)
parameteriza-tion. Masses and widths are in MeV. The first uncertainty is statistical, the second systematic. Also shown are the masses and widths from the PDG [51] Parameter ZEUS PDG Mρ(MeV) 771± 2+2−1 775.49± 0.34 Γρ(MeV) 155± 5 ± 2 149.1± 0.8 β −0.27 ± 0.02 ± 0.02 Mρ(MeV) 1350± 20+20−30 1465± 25 Γρ(MeV) 460± 30+40−45 400± 60 γ 0.10± 0.02+0.02−0.01 Mρ(MeV) 1780± 20+15−20 1720± 20 Γρ(MeV) 310± 30+25−35 250± 100 B 0.41± 0.03 ± 0.07 n 1.30± 0.06+0.18−0.13
• the energy threshold for an unmatched island (elasticity cut) was changed by±50 MeV;
• the bin size in the fitted mass distribution (default 60 MeV) was varied by± 20 MeV;
• the mass range was narrowed to 0.5 < Mπ π<2.3 GeV; • the |t| cut was varied by ±0.1 GeV2;
• the W range was changed to 35 < W < 190 GeV; • the cos θhrange was changed to| cos θh| < 0.9;
• the Wδdependence in the MC was varied by changing the Q2-dependent δ value by±0.03;
• the exponential t distribution in the MC was reweighted by changing the nominal Q2-dependent slope parameter bby±0.5 GeV−2;
• the exponent of the Q2 distribution parameterization in the MC was changed by±0.05.
The largest variations were observed for γ , Γ (ρ)and β. The value of Γ (ρ)changes by 7% when the elasticity cut is varied. The restriction of the phase space in the fitted mass range leads to a change of the value of β by−5.2% while for γ, restricting the| cos θh| range leads to a change of −8%. In addition, another form of background in (6), with an added exponential term, was investigated. It gave a very similar result in the mass range of this analysis and therefore no additional uncertainty was assigned to the form of the fitted mass curve.
All the systematic uncertainties were added in quadra-ture. The combined systematic uncertainties are included in Table1.
8 Decay angular distributions
Decay angular distributions can be used to determine the spin density-matrix elements of a resonance [45,52]. In the present case we study three resonances, all in a JP = 1− state. However, the decay angular distribution in a given mass bin is affected by the background contribution which does not necessarily have the same quantum numbers as the resonance. Given the above, only the distribution of the polar angle θh, defined as the polar angle of the positively charged pion in the helicity frame, was studied.
The distribution of cos θhis shown in Fig.6for different mass bins; its shape is clearly mass dependent. In order to study the mass dependence further, the angular distribution of the polar helicity angle, W (cos θh)was parameterized as
W (cos θh)∝ 1− r + (3r − 1) cos2θh, (8) and fitted to the data. The mass dependence of the resulting parameter r is shown in Fig.7. In the mass range Mπ π < 1.1 GeV, r shows the dependence seen for the r0004 density matrix in the ρ region [2]. Indeed this region is dominated by exclusive production of ρ and therefore r= r0004. In that case, r can be interpreted as σL/σtot, assuming s-channel helicity conservation (SCHC). Here σLis the cross section for producing ρ by a longitudinally polarized photon, and σtot= σL+ σT, with σT the production cross section by transversely polarized photons. The results shown here for the ρ region are in excellent agreement with the values given in an earlier ZEUS paper [2].
The structure seen for Mπ π > 1.1 GeV is not easy to interpret, however the dip observed around 1.3 GeV and the enhancement at 1.6 GeV seem to follow the location of the resonances determined from the mass distribution.
9 Q2dependence of the pion form factor
The Q2 dependence of the relative amplitudes was deter-mined by performing the fit to Mπ π in three Q2 regions, 2–5, 5–10 and 10–80 GeV2. The masses and widths of the three resonances were fixed to the values found in the over-all fit and listed in Table1. The results are shown in Fig.8. A reasonable description of the data is achieved in all three Q2regions. The corresponding values of β and γ are given in Table2. The absolute value of β increases with Q2while the value of γ is consistent with no Q2dependence, within large uncertainties.
Fig. 6 The
acceptance-corrected cos θh distribution for different Mπ π intervals, with the mean mass values indicated in the figure. The lines represent fits to the data as discussed in the text
Table 2 The Q2dependence of the β and γ parameters. Masses and widths are fixed to the values given in Table1. The first uncertainty is statistical, the second systematic
Q2(GeV2) 2–5 5–10 10–80
β −0.249 ± 0.008+0.005−0.003 −0.282 ± 0.008+0.005−0.008 −0.35 ± 0.02 ± 0.01
γ 0.100± 0.009 ± 0.003 0.098± 0.012+0.005−0.003 0.118± 0.022+0.008−0.006
Fig. 7 The fitted parameter r as a function of the two-pion invariant
mass, Mπ π. Only statistical uncertainties are shown
Figure9shows the curves representing the pion form fac-tor,|Fπ(Mπ π)|2, as obtained in the present analysis for the three Q2ranges: 2–5, 5–10, 10–80 GeV2. Also shown are results obtained in the time-like regime from the reaction e+e−→ π+π−. In general, the features of the|Fπ(Mπ π)|2 distribution observed here are also observed in e+e−, i.e., the prominent ρ peak, a shoulder around the ρ and a dip followed by an enhancement in the ρregion. Above the ρ region, where the interference between the ρ and the ρ starts to dominate, there is a dependence of |Fπ(Mπ π)|2 on Q2, with the results from the lowest Q2 range closest to those from e+e−. However, in the region of the ρ peak, shown in Fig.10, the pion form-factor|Fπ(Mπ π)|2is high-est at the highhigh-est Q2, as in the ρ–ρ interference region, while the e+e−data are higher than those in the highest Q2 range. They are equal within errors for Mπ π>1.8 GeV.
10 Cross-section ratios as a function of Q2
The Q2dependence of the ρ by itself is given elsewhere [2]. Since the π π branching ratios of ρ and ρ are poorly
Fig. 8 The two-pion invariant-mass distribution, Mπ π, where Nπ πis
the acceptance-corrected number of events in each bin of 60 MeV, for three regions of Q2, as denoted in the figure. The dots are the data and the full line is the result of a fit using the Kuhn-Santamaria parameteri-zation. The dashed line is the result of the pion form factor normalized to the data and the dash-dotted line denotes the background contribu-tion
known, the ratio RV defined as
RV =
σ (V )· Br(V → ππ)
σ (ρ) , (9)
has been measured, where σ is the cross section for vector-meson production and Br(V → ππ) is the branching ratio of the vector meson V (ρ, ρ)into π π . The ratio RV may be directly determined from the results of the Mπ πmass fit,
Rρ= β2 Iρ Iρ , Rρ= γ2 Iρ Iρ , (10) where IV = MV+5ΓV 2Mπ dMπ πBWV(Mπ π) 2 , (11)
and the integration is carried out over the range 2Mπ < Mπ π< MV + 5ΓV.
Fig. 9 The pion form factor squared, |Fπ|2, as a function of the π+π− invariant mass, Mπ π, as obtained from the reaction
e+e−→ π+π−[19,53,54,56,57]. The shaded bands represent the square of the pion form factor and its total uncertainty obtained in the present analysis for three ranges of Q2: 2–5 GeV2(crossed lines), 5–10 GeV2(horizontal lines) and 10–80 GeV2(vertical lines)
Fig. 10 The pion form factor squared,|Fπ|2, in the ρ mass region, as a
function of the π+π−invariant mass, Mπ π, as obtained from the reac-tion e+e−→ π+π−[19,53,54,56,57]. The shaded bands represent the square of the pion form factor and its total uncertainty obtained in the present analysis for three ranges of Q2: 2–5 GeV2(crossed lines), 5–10 GeV2(horizontal lines) and 10–80 GeV2(vertical lines)
Fig. 11 The ratio RV as a function of Q2 for V = ρ(full circles)
and ρ(open squares). The inner error bars indicate the statistical un-certainty, the outer error bars represent the statistical and systematic uncertainty added in quadrature
Figure11shows and Table3 lists the ratio RV for V = ρ, ρ, as a function of Q2. Owing to the large uncertainties of Rρ, no conclusion on its Q2behaviour can be deduced, whereas Rρ clearly increases with Q2. This rise has been predicted by several models [11,13,16,62,63]. The sup-pression of the 2S state (ρ) is connected to a node effect which results in cancellations of contributions from differ-ent impact-parameter regions at lower Q2, while at higher Q2the effect vanishes.
11 Summary
Exclusive two-pion electroproduction has been studied by ZEUS at HERA in the range 0.4 < Mπ π<2.5 GeV, 2 < Q2<80 GeV2, 32 < W < 180 GeV and |t| ≤ 0.6 GeV2. The mass distribution is well described by the pion elec-tromagnetic form factor,|Fπ(Mπ π)|2, which includes three resonances, ρ, ρ(1450) and ρ(1700).
A Q2dependence of|Fπ(Mπ π)|2is observed, visible in particular in the interference region between ρand ρ. The electromagnetic pion form factor obtained from the present analysis is lower (higher) than that obtained from e+e−→ π+π−for Mπ π<0.8 GeV (0.8 < Mπ π<1.8 GeV). They are equal within errors for Mπ π>1.8 GeV.
The Q2 dependence of the cross-section ratios Rρ = σ (ρ → ππ)/σ (ρ) and Rρ = σ (ρ → ππ)/σ (ρ), has been studied. The ratio Rρ rises strongly with Q2, as ex-pected in QCD-inspired models in which the wave-function
Table 3 The Q2dependence of the ratio RV for V= ρand ρ. The first uncertainty is statistical, the second systematic
Q2(GeV2) 2–5 5–10 10–80
Rρ 0.063± 0.006 ± 0.004 0.081± 0.007+0.006−0.005 0.122± 0.008+0.005−0.006
Rρ 0.027± 0.006+0.004−0.003 0.026± 0.006 ± 0.003 0.039± 0.010+0.003−0.005
of the vector meson is calculated within the constituent quark model, which allows for nodes in the wave-function to be present.
Acknowledgements It is a pleasure to thank the DESY Directorate
for their strong support and encouragement. The remarkable achieve-ments of the HERA machine group were essential for the successful completion of this work and are greatly appreciated. The design, con-struction and installation of the ZEUS detector has been made possible by the efforts of many people who are not listed as authors.
Open Access This article is distributed under the terms of the
Cre-ative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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